Do you have to pay the stimulas check back especially if low income?

No, you will not have to repay the stimulus payment, unless you receive one but turn out not to be eligible when you file your 2020 tax return.

The stimulus payment has been described as an advance on 2020 tax year refundable credits. Does this mean that one should increase the amount of one's estimated tax payments in anticipation of having the amount (s) of stimulus payment(s) subtracted from the total of other payments declared on one's tax return filed in 2021 for the 2020 tax year? 

The IRS has stated it will not try to claw back incorrect stimulus payments.
It is the same as a refund.

the only reason to report stimulus in 2020 is if you got less than you should have, not more.